Precalculus Examples

$\frac{\frac{a}{8} - \frac{4}{a^{2}}}{4}$

Step 1

Simplify the numerator.

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Step 1.1

To write $\frac{a}{8}$ as a fraction with a common denominator, multiply by $\frac{a^{2}}{a^{2}}$ .

$\frac{\frac{a}{8} \cdot \frac{a^{2}}{a^{2}} - \frac{4}{a^{2}}}{4}$

Step 1.2

To write $- \frac{4}{a^{2}}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{\frac{a}{8} \cdot \frac{a^{2}}{a^{2}} - \frac{4}{a^{2}} \cdot \frac{8}{8}}{4}$

Step 1.3

Write each expression with a common denominator of $8 a^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.3.1

Multiply $\frac{a}{8}$ by $\frac{a^{2}}{a^{2}}$ .

$\frac{\frac{a \cdot a^{2}}{8 a^{2}} - \frac{4}{a^{2}} \cdot \frac{8}{8}}{4}$

Step 1.3.2

Multiply $\frac{4}{a^{2}}$ by $\frac{8}{8}$ .

$\frac{\frac{a \cdot a^{2}}{8 a^{2}} - \frac{4 \cdot 8}{a^{2} \cdot 8}}{4}$

Step 1.3.3

Reorder the factors of $a^{2} \cdot 8$ .

$\frac{\frac{a \cdot a^{2}}{8 a^{2}} - \frac{4 \cdot 8}{8 a^{2}}}{4}$

Step 1.4

Combine the numerators over the common denominator.

$\frac{\frac{a \cdot a^{2} - 4 \cdot 8}{8 a^{2}}}{4}$

Step 1.5

Rewrite $\frac{a \cdot a^{2} - 4 \cdot 8}{8 a^{2}}$ in a factored form.

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Step 1.5.1

Multiply $a$ by $a^{2}$ by adding the exponents.

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Step 1.5.1.1

Multiply $a$ by $a^{2}$ .

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Step 1.5.1.1.1

Raise $a$ to the power of $1$ .

$\frac{\frac{a^{1} a^{2} - 4 \cdot 8}{8 a^{2}}}{4}$

Step 1.5.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{\frac{a^{1 + 2} - 4 \cdot 8}{8 a^{2}}}{4}$

Step 1.5.1.2

Add $1$ and $2$ .

$\frac{\frac{a^{3} - 4 \cdot 8}{8 a^{2}}}{4}$

Step 1.5.2

Multiply $- 4$ by $8$ .

$\frac{\frac{a^{3} - 32}{8 a^{2}}}{4}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\frac{a^{3} - 32}{8 a^{2}} \cdot \frac{1}{4}$

Step 3

Multiply $\frac{a^{3} - 32}{8 a^{2}} \cdot \frac{1}{4}$ .

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Step 3.1

Multiply $\frac{a^{3} - 32}{8 a^{2}}$ by $\frac{1}{4}$ .

$\frac{a^{3} - 32}{8 a^{2} \cdot 4}$

Step 3.2

Multiply $4$ by $8$ .

$\frac{a^{3} - 32}{32 a^{2}}$